Question

Taylor series. I'm looking for the first few coefficients (see below). I got the first two right, then I broke it. :P

Answer 1

\[\frac{3x}{1+x} = \sum_{n=0}^{\infty} c_nx^n\]

Answer 2

I did this first :\[c_1=\frac{f'(x)}{1!}=3\] \[c_2=\frac{f''(x)}{2!}=-3\]So far so good. Now: \[c_3=\frac{f'''(x)}{3!}\neq\frac{3}{2}\] Am I just making an arithmetic mistake, or am I misapplying the formula?

Answer 3

i think you did not calculate f'''(x) correctly,
what did u get f'''(x) as ?

Answer 4

because i am getting it as +3

Answer 5

I had\[\frac{f'''3}{3!} = \frac{9(1+x)^{-4}}{3!}\]

Answer 6

hmm, actually, \( f'''(x) = 18 (1+x)^{-4}\)

Answer 7

Oopsie. :)

Answer 8

did you find your error? or still need help

Answer 9

Looking.

Answer 10

Ok, yeah, that was it. Thanks!

Answer 11

welcome ^_^